Skip to main content
SpringerLink
Log in

Application of a wheel–rail contact model to railway dynamics in small radius curved tracks

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

A multibody formulation with Cartesian coordinates is used to describe the kinematic structure of rigid bodies and joints that constitute the vehicle. A track parameterization methodology is implemented for the accurate description of the track spatial geometry emphasizing small radius curves, including its irregularities. A generic formulation is reviewed to determine, during the dynamic analysis, the contact forces that are generated in the wheel–rail interface. This contact model includes an algorithm that identifies the coordinates of the wheel–rail contact points, even for the most general three dimensional motion of the wheelset on the track. The proposed formulation can be applied to study the two points of contact scenario and, since the contact point in the wheel flange does not have to be located in the same plane as the contact point in the tread, it allows analyzing lead and lag flange contact configurations. An elastic force model that allows computing of the normal contact force in the wheel–rail interface, accounting for the energy loss during contact, is implemented and the tangential wheel–rail contact forces are calculated using one of three distinct creep force models: Kalker linear theory; Heuristic nonlinear method; Polach formulation. The methodologies proposed here are demonstrated by their application to the dynamic analysis of the boggie of a metro rail vehicle when negotiating a small radius curved track.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kalker, J.J.: Three-Dimensional Elastic Bodies in Rolling Contact. Kluwer Academic, Dordrecht (1990)

    MATH  Google Scholar 

  2. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    MATH  Google Scholar 

  3. Kik, W., Piotrowski, J.: A fast, approximate method to calculate normal load at contact between wheel and rail and creep forces during rolling. In: Zabory, I. (ed.) 2nd Mini Conference on Contact Mechanics and Wear of Rail/Wheel System, TU Budapest, Hungary (1996)

  4. Shen, Z.Y., Hedrick, J.K., Elkins, J.A.: A comparison of alternative creep force models for rail vehicle dynamic analysis. In: Hedrick, J.K. (ed.) 8th IAVSD Symposium on Dynamics of Vehicles on Road and Tracks, pp. 591–605. Swets and Zeitlinger, Cambridge (1983)

  5. Polach, O.: A fast wheel–rail forces calculation computer code. Veh. Syst. Dyn. Suppl. 33, 728–739 (1999)

    Google Scholar 

  6. Kalker, J.J.: Survey of wheel–rail rolling contact theory. Veh. Syst. Dyn. 8(4), 317–358 (1979)

    Article  Google Scholar 

  7. Kalker, J.J.: Wheel-rail rolling contact theory. J. Wear 144, 243–261 (1991)

    Google Scholar 

  8. Kalker, J.J.: Introduction to the Fortran IV program DUVOROL and CONTACT for the solution of 3D elastostatic half-space contact problems with and without friction. Technical Report of the Department of Mathematics and Informatics No. 82-29, Delft University of Technology, Delft, The Netherlands (1982)

  9. Kalker, J.J.: Book of tables for the hertzian creep-force law. Report of the Faculty of Technical Mathematics and Informatics No. 96-61, Delft University of Technology, Delft, The Netherlands (1996)

  10. Kalker, J.J.: A fast algorithm for the simplified theory of rolling-contact. Veh. Syst. Dyn. 11(1), 1–13 (1982)

    Article  Google Scholar 

  11. Shabana, A.A., Zaazaa, K.E., Escalona, J.L., Sany, J.R.: Dynamics of the wheel/rail contact using a new elastic force model. Technical Report #MBS02-3-UIC, Department of Mechanical Engineering, University of Illinois, Chicago (2002)

  12. Shabana, A.A., Zaazaa, K.E., Escalona, J.L., Sany, J.R.: Modeling two-point wheel/rail contacts using constraint and elastic-force approaches. In: Proceedings of the IMECE’02: 2002 ASME International Mechanical Engineering Congress and Exposition, New Orleans, Louisiana, 17–22 November 2002

  13. Pombo, J., Ambrósio, J., Silva, M.: A new wheel–rail contact model for railway dynamics. Veh. Syst. Dyn. 45(2), 165–189 (2007)

    Article  Google Scholar 

  14. Pombo, J., Ambrósio, J.: A multibody methodology for railway dynamics applications. Technical Report IDMEC/CPM—2004/003, IDMEC—Institute of Mechanical Engineering, Instituto Superior Técnico, Lisbon, Portugal (2004)

  15. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. AMSE J. Mech. Des. 112, 369–376 (1990)

    Google Scholar 

  16. Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)

    Google Scholar 

  17. Kalker, J.J.: Simplified theory of rolling contact. In: Progress Report Series C: Mechanical and Aeronautical Engineering and Shipbuilding, vol. 1, pp. 1–10. Delft University of Technology, Delft (1973)

    Google Scholar 

  18. Kalker, J.J.: The computation of three-dimensional rolling contact with dry friction. Numer. Method. Eng. 14(9), 1293–1307 (1979)

    Article  MATH  Google Scholar 

  19. Pombo, J., Ambrósio, J.: General spatial curve joint for rail guided vehicles: kinematics and dynamics. Multibody Syst. Dyn. 9, 237–264 (2003)

    Article  MATH  Google Scholar 

  20. Pombo, J., Ambrósio, J.: Development of a roller coaster model. In: Schiehlen, W., Valasek, M. (eds.) Proceedings of the NATO-ASI on Virtual Nonlinear Multibody Systems, vol. 2, pp. 195–203. Prague, Czech Republic, 23 June–3 July 2002

  21. Pombo, J., Ambrósio, J.: Development of a roller coaster model. In: Goicolea, J. et al. (eds.) Proceedings of the Métodos Numéricos en Ingeniería V, SEMNI, Madrid, Spain, 3–6 June 2002

  22. Nikravesh, P.E.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs, New Jersey (1988)

    Google Scholar 

  23. Mortenson, M.E.: Geometric Modeling. Wiley, New York (1985)

    Google Scholar 

  24. Pombo, J., Ambrósio, J.: A general track model for rail guided vehicles dynamics. In: Barbosa, J.I. (ed.) Proceedings of the VII Congresso de Mecânica Aplicada e Computacional, vol. 2, pp. 47–56. Évora, Portugal, 14–16 April 2003

  25. Pombo, J., Ambrósio, J.: A wheel–rail contact model for rail guided vehicles dynamics. In: Ambrósio, J. (ed.) Proceedings of the ECCOMAS Thematic Conference on Advances in Computational Multibody Dynamics, Lisbon, Portugal, 1–4 July 2003

  26. Berzeri, M., Sany, J.R., Shabana, A.A.: Curved track modeling using the absolute nodal coordinate formulation. Technical Report #MBS00-4-UIC, Department of Mechanical Engineering, University of Illinois, Chicago (2000)

  27. De Boor, C.: A Practical Guide to Splines. Springer, New York (1978)

    MATH  Google Scholar 

  28. Visual Numerics, Inc. In: IMSL Fortran 90 Math Library 4.0—Fortran Subroutines for Mathematical Applications. Huston, Texas (1997)

  29. Irvine, L.D., Marin, S.P., Smith, P.W.: Constrained interpolation and smoothing. Constr. Approx. 2, 129–151 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  30. Micchelli, C.A., Smith, P.W., Swetits, J., Ward, J.D.: Constrained Lp approximation. Constr. Approx. 1, 93–102 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  31. Kassa, E., Andersson, C., Nielsen, J.: Simulation of dynamic interaction between train and railway turnout. Veh. Syst. Dyn. 44(3), 247–258 (2006)

    Article  Google Scholar 

  32. Shabana, A.A., Berzeri, M., Sany, J.R.: Numerical procedure for the simulation of wheel/rail contact dynamics. J. Dyn. Syst. Meas. Control Trans. ASME 123(2), 168–178 (2001)

    Article  Google Scholar 

  33. Johansson, A., Andersson, C.: Out-of-round railway wheels—a study of wheel poligonization through simulation of three-dimensional wheel–rail interaction and wear. Veh. Syst. Dyn. 43(8), 539–559 (2005)

    Article  Google Scholar 

  34. Pombo, J., Ambrósio, J.: Dynamic analysis of railway vehicles. In: Soares, C.M., et al. (eds.) Proceedings of the VIII Congresso de Mecânica Aplicada e Computacional APMTAC, SEMNI, Lisbon, Portugal, 31 May–2 June 2004

  35. Pombo, J., Ambrósio, J.: A computational efficient general wheel–rail contact detection method. J. Mech. Sci. Technol. 19(1), 411–421 (2005), the separate volume of KSME International Journal, Special Edition

    Article  Google Scholar 

  36. Roberson, R.E., Schwertassek, R.: Dynamics of Multibody Systems. Springer, Berlin (1988)

    MATH  Google Scholar 

  37. Andersson, E., Berg, M., Stichel, S.: Rail Vehicle Dynamics, Fundamentals and Guidelines. Royal Institute of Technology (KTH), Stockholm (1998)

    Google Scholar 

  38. Quost, X., Sebes, M., Eddhahak, A., Ayasse, J.-B., Chollet, H., Gautier, P.-E., Thouverez, F.: Assessment of semi-hertzian method for determination of wheel–rail contact patch. Veh. Syst. Dyn. 43(8), 539–559 (2005)

    Article  Google Scholar 

  39. Alonso, A., Gimenez, J.G.: Tangential problem solution for non-elliptical contact areas with the fastsim algorithm. Veh. Syst. Dyn. 45(10), 789–814 (2006)

    Google Scholar 

  40. Goldsmith, W.: Impact—The Theory and Physical Behaviour of Colliding Solids. Edward Arnold, London (1960)

    MATH  Google Scholar 

  41. Pombo, J., Ambrósio, J.: Modelação de veículos ferroviários da CP e do metropolitano de Lisboa. Technical Report No. 19 of PEDIP Project No. 25/00379 on “Dinâmica de Veículos Ferroviários”, Lisbon, Portugal (2000)

  42. Dukkipati, R.V., Amyot, J.R.: Computer-Aided Simulation in Railway Dynamics. Dekker, New York (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IDMEC—Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    João C. Pombo & Jorge A. C. Ambrósio

Authors
  1. João C. Pombo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jorge A. C. Ambrósio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to João C. Pombo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pombo, J.C., Ambrósio, J.A.C. Application of a wheel–rail contact model to railway dynamics in small radius curved tracks. Multibody Syst Dyn 19, 91–114 (2008). https://doi.org/10.1007/s11044-007-9094-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-007-9094-y

Keywords

Search

Navigation